%I #13 Sep 08 2022 08:46:12

%S 43,257,12113,84131,96137,168143,372167,32041181,120409349,139129379,

%T 292681547,410881643,516961727,528529733,863041937,966289991,

%U 10629611033,10670891039,11902811093,16307291279,21112091459,25058891597,29618411723,31933691789,35006411873

%N Primes formed by concatenating p^2 with q, where p, q are consecutive primes.

%C All the terms in this sequence, except a(1), are congruent to 2 (mod 3).

%H K. D. Bajpai, <a href="/A258214/b258214.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2) = 257 is prime formed by concatenation of (5^2) = 25 with 7.

%e a(3) = 12113 is prime formed by concatenation of (11^2) = 121 with 13.

%t Select[Table[p = Prime[n]; FromDigits[Join[Flatten[ IntegerDigits[{p^2, NextPrime[p]}]]]], {n, 500}], PrimeQ]

%t Select[#[[1]]^2*10^IntegerLength[#[[2]]]+#[[2]]&/@Partition[Prime[ Range[ 300]],2,1],PrimeQ] (* _Harvey P. Dale_, Dec 05 2016 *)

%o (PARI) forprime(p = 1,5000, k=eval(concat( Str(p^2), Str(nextprime(p+1)) )); if(isprime(k), print1(k,", ")))

%o (Magma) [m: n in [1..300] | IsPrime(m) where m is Seqint(Intseq(NthPrime(n+1)) cat Intseq(NthPrime(n)^2))]; // _Vincenzo Librandi_, May 24 2015

%Y Cf. A000040, A030461, A030469.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, May 23 2015